Theoretical and methodological challenges in hierarchical Bayesian inference for model-form uncertainty

Technical Report · Mon Sep 01 04:00:00 EDT 2025

DOI:https://doi.org/10.2172/2587508· OSTI ID:2587508

Portone, Teresa ^[1]; White, Rebekah Dale ^[1]

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1. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

This report describes challenges associated with the hierarchical Bayesian approach to inform model-form uncertainty (MFU) representations, which are parameterized modifications to a mathematical models’ governing equations to express uncertainty in form of the equations. To inform model-form uncertainties, hierarchical Bayesian inference is often employed. Here, the MFU parameters are distributed parametrically, and the hyperparameters of the parametric distribution are informed through Bayesian inference, with the aim of determining the MFU parameter distribution that best agrees with calibration data. In practice, however, we have found the hierarchical Bayesian approach falls short of this aim. We discuss theoretical and methodological challenges of the approach, and we present several numerical demonstrations of these challenges. To conclude, we suggest promising alternative approaches for future investigation.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
• DOE Contract Number: NA0003525
• OSTI ID: 2587508
• Report Number(s): SAND--2025-10780; 1787643
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING